We discuss the rigidity of Einstein manifolds and generalized quasi-Einstein manifolds. We improve a pinching condition used in a theorem on the rigidity of compact Einstein manifolds. Under an additional condition, we confirm a conjecture on the rigidity of compact Einstein manifolds. In addition, we prove that every closed generalized quasi-Einstein manifold is an Einstein manifold provided μ = -1/(n-2), λ ≤ 0 and β ≤ 0.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap115-3-3,
author = {Yi Hua Deng and Li Ping Luo and Li Jun Zhou},
title = {Rigidity of Einstein manifolds and generalized quasi-Einstein manifolds},
journal = {Annales Polonici Mathematici},
volume = {113},
year = {2015},
pages = {235-240},
zbl = {1337.53054},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap115-3-3}
}
Yi Hua Deng; Li Ping Luo; Li Jun Zhou. Rigidity of Einstein manifolds and generalized quasi-Einstein manifolds. Annales Polonici Mathematici, Tome 113 (2015) pp. 235-240. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap115-3-3/